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Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other. Q.6

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Please give me the best way for solving the problem of class 9th ncert math of Quadrilaterals chapter of math of class 9th of exercise 8.2 of question no 6 what is the tricky way for solving this question Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

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  1. :

    Ncert solutions class 9 chapter 8-17

    Let ABCD be a quadrilateral and P, Q, R and S are the mid points of AB, BC, CD and DA respectively.

    Now,

    In ΔACD,

    R and S are the mid points of CD and DA respectively.

    , SR || AC.

    Similarly we can show that,

    PQ || AC,

    PS || BD and

    QR || BD

    , PQRS is parallelogram.

    PR and QS are the diagonals of the parallelogram PQRS. So, they will bisect each other.

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